Question

A metallurgist purchases a car for total cost including tax and license of $31,795.66. If the metallurgist obtains a 4-year loan at an annual interest rate of 4.4% compounded monthly, what is the monthly car payment (in dollars? (Round your answer to the nearest cent. See Example 1 in this section.)

Answer 1

the monthly car payment is $722.91

Explanation:

To find the monthly car payment, we need to use the formula for the monthly payment of a loan:

P = (Pr(1+r)^n)/((1+r)^n - 1)

where P is the monthly payment, P is the loan principal (the total cost of the car including tax and license), r is the monthly interest rate, and n is the total number of payments (the number of years multiplied by 12 months per year).

First, we need to convert the annual interest rate of 4.4% to a monthly interest rate. We divide 4.4% by 12 to get:

r = 0.044/12 = 0.0036667

Next, we need to calculate the total number of payments. Since the loan is for 4 years and there are 12 months in a year, the total number of payments is:

n = 4 years x 12 months/year = 48

Now we can substitute the values into the formula:

P = (31795.66(0.0036667)(1+0.0036667)^48)/((1+0.0036667)^48 - 1)

Using a calculator, we get:

P = $722.91 (rounded to the nearest cent)

Therefore, the monthly car payment is $722.91.